Credit Risk Fundamentals

Lend a friend $1,000 for a year at five percent and look honestly at your two outcomes. If everything goes well you end up $50 richer. If it goes badly you can lose the whole $1,000. There is no version of the story where you make $400, no matter how well your friend's year turns out. That shape, a small capped gain against a large possible loss, is what makes lending fundamentally different from owning equity, and credit risk is the discipline built around it.

It matters because almost every institution is a lender whether it thinks so or not. A bank making loans, obviously. But also a bond fund, a clearing house holding your margin, a supplier shipping goods on thirty-day terms, and a trading desk with an open swap against a counterparty. All of them have handed something over and are waiting to be made whole.

The three questions

Every credit loss, from a corporate bankruptcy to an unpaid invoice, decomposes the same way.

• Probability of default ($PD$) — how likely is the borrower to fail to pay over some stated horizon, usually one year. Roughly $0.05\%$ for a top-rated corporate; several percent for a stressed high-yield issuer.
• Loss given default ($LGD$) — if they do fail, what fraction of the exposure do you actually lose after the bankruptcy process returns something to you. It is simply one minus the recovery rate.
• Exposure at default ($EAD$) — how much are you owed at that moment. Fixed for a bond, but for a credit line or a swap it is whatever has been drawn or has moved in your favour by then.

Multiply them and you get the expected loss, the average cost of lending per year:

$$EL = PD \times LGD \times EAD.$$

In words: the chance it goes wrong, times how bad it is when it does, times how much is on the table. Each term answers a genuinely different question, and confusing any two of them is the most common error in credit.

Worked example: pricing the same borrower twice

Take a company with a one-year $PD$ of $2\%$. You hold a $10m senior unsecured bond, and historical recoveries on that kind of debt run near $40\%$, so $LGD = 60\%$.

$$EL = 0.02 \times 0.60 \times 10{,}000{,}000 = 120{,}000 .$$

That is $120,000 a year, $1.2\%$ of the loan. If the bond pays a spread of $2\%$ over Treasuries, $200,000 a year, then $120,000 of that is not really income at all: it is the fee you must set aside to cover average defaults. Only the remaining $80,000 is genuine compensation.

Now the same company, same year, but you hold a $10m secured loan backed by real collateral. The $PD$ is identical, because it is the same firm going bankrupt. But recoveries on senior secured debt run near $75\%$, so $LGD = 25\%$:

$$EL = 0.02 \times 0.25 \times 10{,}000{,}000 = 50{,}000 ,$$

just $0.5\%$. The secured lender can happily accept less than half the spread for lending to exactly the same company. That single comparison explains why debt is issued in layers and why Seniority and the Capital Stack is priced so carefully.

Expected loss is not the risk

Here is the catch. Expected loss is an average, and averages are what you budget for, not what kills you. Rerun the first example in a recession: $PD$ triples to $6\%$ and recoveries fall, pushing $LGD$ to $75\%$. Now $EL = 0.06 \times 0.75 \times 10{,}000{,}000 = 450{,}000$, nearly four times the calm-weather number. The gap between what you provisioned and what actually happened is unexpected loss, and it is what capital exists to absorb.

Notice why that year was so bad: $PD$ and $LGD$ both got worse at the same time. Defaults cluster, because firms fail for shared reasons, and the assets seized in a bust are worth less precisely because everyone is selling them at once.

What this means in practice

Credit risk shows up in more forms than outright default. Migration risk is a downgrade that widens your Credit Spreads and marks your bond down without anyone missing a payment. Counterparty risk is a derivatives partner failing while a trade is in your favour. Concentration risk is holding twenty loans to the same industry and calling it a diversified book. In practice, quants meet credit risk as a spread on a screen, a rating in a database, and a correlated loss distribution in a portfolio model.

Key terms

• Default — failure to meet an obligation, from a missed coupon to bankruptcy.
• PD / LGD / EAD — probability of default, loss given default, exposure at default.
• Expected loss — the product of the three; a cost of doing business, not a risk measure.
• Unexpected loss — how far a bad year exceeds that average; what capital covers.
• Migration risk — losses from downgrades and spread widening rather than default itself.